Strong Convergence Theorems According. to a New Iterative Scheme with Errors for. Mapping Nonself I-Asymptotically. Quasi-Nonexpansive Types
|
|
- Candice Hodges
- 5 years ago
- Views:
Transcription
1 It. Joural of Math. Aalysis, Vol. 4, 00, o. 5, Strog Covergece Theorems Accordig to a New Iterative Scheme with Errors for Mappig Noself I-Asymptotically Quasi-Noexpasive Types Narogrit Puturog Mathematics Program, Faculty of Sciece Udo Thai Rajabhat Uiversity, Udo Thai 4000, Thailad aputurog@hotmail.com Abstract I this paper, a ew iterative scheme with errors for mappig oself I- asymptotically quasi-oexpasive types ad oself I-asymptotically quasioexpasive types i Baach space is defied. The results obtaied i this paper exted ad improve upo those recetly aouced by S.S.Yao ad L.Wag [ Yao & Wag, (008) : Strog Covergece Theorems for Noself I-Asymptotically Quasi-Noexpasive Mappigs, published i Applied Mathematical Scieces 9(008 : 99-98) ] amog others. Mathematics Subject Classificatio: 46C05, 47H05, 47H09, 47H0 Keywords: Noself I-asymptotically quasi-oexpasive type mappig; Completely cotiuous; Uiformly covex Baach apace; Uiformly L- Lipschitzia. Itroductio Let X be a real Baach space ad let C be a oempty subset of X, P : X C be a oexpasive retractio of X oto C. A oself mappig T : C X is called asymptotically oexpasive [] if there exists a sequece {k } [, ) with k as such that for each, T(PT) x T(PT) y k x - y, for all x, y C. T is said to be uiformly L- Lipschitzia if there exists a costat L > 0 such that T(PT) x T(PT) y L x - y, for all x, y C.
2 38 N. Puturog T : C X is completely cotiuous [] if for all bouded sequeces {x } C there exists a coverget subsequece of {Tx }. Recallig that a Baach space X is called uiformly covex [5] if, for x + y every 0 < ε, there exists δ δ( ε) > 0 such that δ for every x, y S X ad x y ε, S X {x X : x }. Let T, I : C C, the T is called I-oexpasive o C [4] if Tx Ty Ix Iy for all x, y C. T is called I-asymptotically oexpasive o C if there exists a sequece { λ k } [0, ) with λ k 0 as k such that T k x T k y ( λ k +) I k x I k y, for all x, y C ad k,, 3, T is called I-asymptotically quasi-oexpasive o C [7] if there exists a sequece { λ k } [0, ) with λ k 0 as k such that T k x f ( λ k +) I k x f, for all x C ad k 0 ad for every f F(T) F(I), where φ F(T) F(I) be the set of all commo fixed poits of T ad I. Let T, I : C X, the T is called oself I-asymptotically quasi-oexpasive [6] if there exists a sequece {k } [, ) with k as such that for each, T(PT) x f k I(PI) x f, for all x C ad f F(T) F(I), where P is a retractio from X oto C. I 004, N.Shahzad [4] itroduced the cocept of I-oexpasive mappig i Baach space. I 007, S.Temir ad O.Gul [7] defied I-asymptotically quasioexpasive mappig ad studied the weak covergece theorems for I-asymptotically quasi-oexpasive mappig i Hilbert space. More recetly, S.S.Yao ad L.Wag [6] defied oself I-asymptotically quasi-oexpasive mappig ad proved some strog covergece theorems for such mappig i uiformly covex Baach spaces. The purpose of this paper is to itroduce the cocept of oself I-asymptotically quasi-oexpasive types ad strog covergece theorems, ad defie a ew iterative scheme with errors which modified the iterative scheme of S.S.Yao ad L.Wag [6].. Prelimiaries Let C be a oempty subset of a Baach space X. A subset C is called retract of X if there exists cotiuous mappig P : X C such that Px x for all x C. It is well kow that every closed covex subset of a uiformly covex Baach space is a retract. A mappig P : X C is called a retractio if P P. Note that if a mappig P is a retractio, the Pz z for all z i the rage of P.
3 Strog covergece theorems 39 Let X be a real Baach space ad let C be a oempty closed covex subset of X. Let P : X C be a retractio of X oto C ad let I : C X be a oself mappig ad T : C X be a oself I-asymptotically quasi-oexpasive type as defied by defiitio 3.. Algorithm. For a give x C, we compute the sequece {x } by the iterative scheme x + P(a I(PI) y + ( a b )x + b u ) y P(c T(PT) x + ( c d )x + d v ),, where {u }, {v } are bouded sequeces i C ad {a }, {b }, {c }, {d }, {a + b } ad {c + d } are appropriate sequeces i [0, ]. (.) If b 0 ad d 0, the (.) is reduced to the iterative scheme defied by S.S.Yao ad L.Wag [6], as follows: Algorithm. For a give x C, we compute the sequece {x } by the iterative scheme x + P(a I(PI) y + ( a )x ) y P(c T(PT) x + ( c )x ),, where {a }, {c } are appropriate sequeces i [0, ]. (.) Recallig a well-kow cocept, ad the followig essetial lemmas, i order to prove our mai results: Lemma. [3]. Let {a }, {b } ad { δ } be sequeces of oegative real umbers satisfyig the iequality a + ( + δ )a + b,,, It δ < ad b <, the lim a exists. Lemma. []. Let X be a real uiformly covex Baach space ad 0 p t q < for all positive itegers. Also suppose that {x } ad {y } are two sequeces of X such that limsup x r, limsup y r ad limsup t x + ( t )y r hold for some r 0, the lim x y Mai Results I this sectio, we provide proof of a covergece theorem for a ew iterative scheme with errors for a mappig of oself I-asymptotically quasioexpasive types. I providig such proof of our mai results, the followig defiitio ad lemmas are required:
4 40 N. Puturog Defiitio 3.. Let C be a oempty closed covex subset of real Baach space X. T : C X be a oself I-asymptotically quasi-oexpasive mappig, I : C X be a oself mappig, φ F(T) F(I) be the set of all commo fixed poits of T ad I. T is called a oself I-asymptotically quasi-oexpasive type mappig if T is uiformly cotiuous, ad limsup{sup( T(PT ) x q I( PI) x q )} 0, for all q F(T) F(I), where P is a retractio from X oto C. Lemma 3.. Let C be a oempty subset of a real Baach space X. Let T : C X be a oself I-asymptotically quasi-oexpasive type, I : C X be a oself asymptotically oexpasive mappig with sequece {k } [, ), (k ) <, P be a retractio from X oto C. Put G max {0, sup( T(PT ) x q I( PI ) x q ) },, q F(T) F(I), so that G <. Suppose that sequece {x } is geerated by (.) with b < ad d <. If F(T) F(I) φ, the lim x q exists for ay q F(T) F(I). Proof. Settig k + r. Sice (k ) <, so r <. Let q F(T) F(I), ad M sup{ u - q : }, M sup{ v - q : }. Usig (.) with b < ad d <, we have x + q P(a I(PI) y + ( a b )x + b u ) q a I(PI) y q + ( a b ) x q + b u q a k y q + ( a b ) x q + b u q a k P(c T(PT) x + ( c d )x + d v ) q + ( a b ) x q + b u q a k c (T(PT) x q) + ( c d )(x q) + d (v q) + ( a b ) x q + b M a k c ( T(PT) x q + a k ( c d ) x q + a k d v q + ( a b ) x q + b M a k c ( T(PT) x q - I(PI) x q + a k c I(PI) x q + a k ( c d ) x q + a k d v q + ( a b ) x q + b M
5 Strog covergece theorems 4 a k c sup { T(PT) x q - I(PI) x q } + a k k c x q + a k ( c d ) x q + a k d M + ( a b ) x q + b M a k c G + [a c k + a k ( c d ) + ( a b )] x q + a k d M + b M [a c ( + r ) + a ( + r ) a c ( + r ) a d ( + r ) + a b ] x q + a c ( + r )G + a d ( + r )M + b M [a c r + a c r + a r a d a d r + b ] x q + a c ( + r )G + a d ( + r )M + b M [ + r + r + r ] x q + ( + r )G + ( + r )d M + b M [ + (r + r )] x q + s, (3.) where s ( + r )G + ( + r )d M + b M. Sice r <, G <, b < ad d <, we see that ( r + r ) < ad s <. If follows from Lemma. that lim x q exists. This completes the proof. # Lemma 3.. Let X be a uiformly covex Baach space. Let C, T, I ad {x } be same as i Lemma 3.. Put G max {0, sup( T(PT ) x q I( PI) x q ) },, q F(T) F(I), so that G <. If T is uiformly L-Lipschitzia for some L > 0 ad F(T) F(I) φ, the lim Tx x lim Ix x 0. Proof. By Lemma 3., for ay q F(T) F(I), bouded. Assume lim x q t 0. Let M sup{ u q : } ad M sup{ v q : }. Usig (.) with b < ad d lim x <, we have q exists, the {x } is y q P(c T(PT) x + ( c d )x + d v ) q c T(PT) x q + ( c d ) x q + d v q c ( T(PT) x q - I(PI) x q ) + c I(PI) x q + ( c d ) x q + d M c sup { T(PT) x q - I(PI) x q ) + c k x q
6 4 N. Puturog + ( c d ) x q + d M c G + c ( + r ) x q + ( c d ) x q + d M c G + (c r + d ) x q + d M ( + r ) x q + G + d M ( + r ) x q + e, (3.) where e G + d M. Sice G < ad d <, so that e <. Takig lim sup o both sides i above iequality, we obtai lim sup y q t. (3.3) Sice I(PI) y q ( + r ) y q. Takig lim sup o both sides i above iequality ad usig (3.3), we have Sice lim sup I(PI) y q t. lim x + q t, the t lim P(a I(PI) y + ( a b )x + b u ) q lim a (I(PI) y q) + ( a b )(x q)+ b (u q) lim [ a (I(PI) y q)+( a )(x q) ] -lim b x q + Sice b <, so that lim b x q 0 ad lim b M 0, we have t lim [ a (I(PI) y q) + ( a )(x q) ]. Similarly, for proof (3.), we have Sice lim a (I(PI) y q) + ( a )(x q) lim x q + r <, lim ( + r )G 0 ad t lim(r + G < ad d r ) x q + lim ( + r )G + <, we see that lim ( + r )d M 0. We have lim a (I(PI) y q) + ( a )(x q) lim b M. lim ( + r )d M. lim(r+ r ) x q 0, lim x q t so that lim a (I(PI) y q) + ( a )(x q) t. It follows from Lemma. that, lim I(PI) y x 0. (3.4) Next, x - q x I(PI) y + I(PI) y q x I(PI) y + ( + r ) y q gives that t lim x - q lim if y q. By (3.3), we have
7 Strog covergece theorems 43 So that t lim y q t. lim P(c T(PT) x + ( c d )x + d v ) q lim ( c (T(PT) x q) + ( c )(x q) - + lim d v q lim d x q lim ( c (T(PT) x q) + ( c )(x q) Similarly, for proof (3.), we have t lim ( c (T(PT) x q) + ( c )(x q) lim x q t. So that lim ( c (T(PT) x q) + ( c )(x q) t. (3.5) Next, T(PT) x q T(PT) x q - I(PI) x q + I(PI) x q sup ( T(PT) x q - I(PI) x q ) + I(PI) x q Sice G <, we have lim G + ( + r ) x q G + x q + r x q. r < ad lim sup x q t, sup T(PT) x q t. (3.6) By (3.5), (3.6), lim sup x q t ad Lemma., we have lim T(PT) x x 0. (3.7) Also, I(PI) x x I(PI) x I(PI) y + I(PI) y x ( + r ) x y + I(PI) y x ( + r ) c (x T(PT) x ) + d ( x q + q v ) + I(PI) y x c ( + r ) x T(PT) x + d ( x q + M ) + I(PI) y x. Thus by (3.4), (3.7) ad d <, we have lim I(PI) x x 0. (3.8) Sice I(PI) x T(PT) x I(PI) x x + x - T(PT) x I(PI) x x + x T(PT) - x. It follows from (3.7) ad (3.8) that lim I(PI) x T(PT) x 0. (3.9) I additio, x + x a I(PI) y x + b u x a I(PI) y x + b ( u q + q x ) a I(PI) y x + b (M + q x ) Thus by (3.4) ad b <, we have
8 44 N. Puturog lim x + x 0. (3.0) Sice I(PI) y x + I(PI) y x + x x +, by (3.4) ad (3.0), we have lim I(PI) y x + 0. (3.) So, x + y x + I(PI) y + I(PI) y y x + I(PI) y + I(PI) y x + x y x + I(PI) y + I(PI) y x + y x x + I(PI) y + I(PI) y x + P(c T(PT) x + ( c d )x + d v ) x x + I(PI) y + I(PI) y x + c T(PT) - x x + d v x. Usig (3.4), (3.7), (3.) ad d <, we have lim x + y 0. (3.) Ix x Ix I(PI) y + I(PI) y I(PI) x + I(PI) x x Ix I(PI) y + I(PI) y I(PI) x + I(PI) x x ( + r ) x I(PI) y + (+ r ) y x + I(PI) x x. It follows from (3.8), (3.) ad (3.), we obtai lim Ix x 0. (3.3) Sice T is uiformly L-Lipschitzia for some L > 0, Tx x Tx T(PT) x + T(PT) x x Tx T(PT) x + T(PT) x x L x T(PT) x + T(PT) x x L[ x x - + x - T(PT) x + T(PT) x T(PT) x ] + T(PT) x x L x - T(PT) x + (L + L) x x - + T(PT) x x. Usig (3.7) ad (3.0), we have lim Tx x 0. (3.4) This completes the proof. # Theorem 3.3. Let X, C, T, I ad {x } be same as i Lemma 3.. Put G max {0, sup( T(PT ) x q I( PI) x q ) },, q F(T) F(I), so that G <. If I is completely cotiuous ad F(T) F(I) φ, the {x } is coverged strogly to a commo fixed poit of T ad I. Proof. From Lemma 3., we kow that lim x q exists for ay q F(T) F(I), the {x } is bouded. By Lemma 3., we have
9 Strog covergece theorems 45 lim Tx x 0 ad lim Ix x 0. (3.5) Suppose that I is completely cotiuous, ad otig that {x } is bouded: We coclude that subsequece { Ix } of {Ix j } exists, such that { Ix } coverges. j Therefore, from (3.5), { x } is coverged. Let x j r as j. From the j cotiuity of P, T, I ad (3.5), we have r Tr Ir. Thus, {x } is coverged strogly to a commo fixed poit r of T ad I. This completes the proof. # Refereces [] C.E. Chidume, E.U. Ofoedu ad H. Zegeye, Strog ad weak covergece theorems for asymptotically oexpasive mappigs, J. Math. Aal. Appl., 80(003), [] J. Schu, Iterative costructio of fixed poit of asymptotically oexpasive mappigs, Joural of Mathematical Aalysis ad Applicatios, 58(99), [3] K. K. Ta ad H. K. Xu, Approximatig fixed poits of oexpasive mappig by the Ishikawa iteratio process, Joural of Mathematical Aalysis ad Applicatios, 78(993), [4] N. Shahzad, Geeralized I-oexpasive maps ad best approximatios i Baach spaces, Demostratio Math. XXXVII(3)(004), [5] Robert E. Meggiso, A Itroductio to Baach Space Theory, Spriger- Verlag New York, 998. [6] S.S. Yao ad L. Wag, Strog covergece theorems for oself I- asymptotically quasi-oexpasive mappigs, Applied Mathematical Scieces, 9(008), [7] S. Temir ad O. Gul, Covergece theorems for I- asymptotically quasioexpasive mappig i Hilbert space, J. Math. Aal. Appl. 39(007), Received: Jauary, 00
On Weak and Strong Convergence Theorems for a Finite Family of Nonself I-asymptotically Nonexpansive Mappings
Mathematica Moravica Vol. 19-2 2015, 49 64 O Weak ad Strog Covergece Theorems for a Fiite Family of Noself I-asymptotically Noexpasive Mappigs Birol Güdüz ad Sezgi Akbulut Abstract. We prove the weak ad
More informationWeak and Strong Convergence Theorems of New Iterations with Errors for Nonexpansive Nonself-Mappings
doi:.36/scieceasia53-874.6.3.67 ScieceAsia 3 (6: 67-7 Weak ad Strog Covergece Theorems of New Iteratios with Errors for Noexasive Noself-Maigs Sorsak Thiawa * ad Suthe Suatai ** Deartmet of Mathematics
More informationA General Iterative Scheme for Variational Inequality Problems and Fixed Point Problems
A Geeral Iterative Scheme for Variatioal Iequality Problems ad Fixed Poit Problems Wicha Khogtham Abstract We itroduce a geeral iterative scheme for fidig a commo of the set solutios of variatioal iequality
More informationResearch Article Convergence Theorems for Finite Family of Multivalued Maps in Uniformly Convex Banach Spaces
Iteratioal Scholarly Research Network ISRN Mathematical Aalysis Volume 2011, Article ID 576108, 13 pages doi:10.5402/2011/576108 Research Article Covergece Theorems for Fiite Family of Multivalued Maps
More informationConvergence of Random SP Iterative Scheme
Applied Mathematical Scieces, Vol. 7, 2013, o. 46, 2283-2293 HIKARI Ltd, www.m-hikari.com Covergece of Radom SP Iterative Scheme 1 Reu Chugh, 2 Satish Narwal ad 3 Vivek Kumar 1,2,3 Departmet of Mathematics,
More informationResearch Article On Common Random Fixed Points of a New Iteration with Errors for Nonself Asymptotically Quasi-Nonexpansive Type Random Mappings
Iteratioal Joural of Aalysis Volume 2013, Article ID 312685, 10 pages http://dx.doi.org/10.1155/2013/312685 Research Article O Commo Radom Fixed Poits of a New Iteratio with Errors for Noself Asymptotically
More informationON A CLASS OF SPLIT EQUALITY FIXED POINT PROBLEMS IN HILBERT SPACES
J. Noliear Var. Aal. (207), No. 2, pp. 20-22 Available olie at http://jva.biemdas.com ON A CLASS OF SPLIT EQUALITY FIXED POINT PROBLEMS IN HILBERT SPACES SHIH-SEN CHANG,, LIN WANG 2, YUNHE ZHAO 2 Ceter
More informationIterative Method For Approximating a Common Fixed Point of Infinite Family of Strictly Pseudo Contractive Mappings in Real Hilbert Spaces
Iteratioal Joural of Computatioal ad Applied Mathematics. ISSN 89-4966 Volume 2, Number 2 (207), pp. 293-303 Research Idia Publicatios http://www.ripublicatio.com Iterative Method For Approimatig a Commo
More informationCouncil for Innovative Research
ABSTRACT ON ABEL CONVERGENT SERIES OF FUNCTIONS ERDAL GÜL AND MEHMET ALBAYRAK Yildiz Techical Uiversity, Departmet of Mathematics, 34210 Eseler, Istabul egul34@gmail.com mehmetalbayrak12@gmail.com I this
More informationThe value of Banach limits on a certain sequence of all rational numbers in the interval (0,1) Bao Qi Feng
The value of Baach limits o a certai sequece of all ratioal umbers i the iterval 0, Bao Qi Feg Departmet of Mathematical Scieces, Ket State Uiversity, Tuscarawas, 330 Uiversity Dr. NE, New Philadelphia,
More informationSome iterative algorithms for k-strictly pseudo-contractive mappings in a CAT (0) space
Some iterative algorithms for k-strictly pseudo-cotractive mappigs i a CAT 0) space AYNUR ŞAHİN Sakarya Uiversity Departmet of Mathematics Sakarya, 54187 TURKEY ayuce@sakarya.edu.tr METİN BAŞARIR Sakarya
More informationFixed Point Theorems for Expansive Mappings in G-metric Spaces
Turkish Joural of Aalysis ad Number Theory, 7, Vol. 5, No., 57-6 Available olie at http://pubs.sciepub.com/tjat/5//3 Sciece ad Educatio Publishig DOI:.69/tjat-5--3 Fixed Poit Theorems for Expasive Mappigs
More informationSOME SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS
ARCHIVU ATHEATICU BRNO Tomus 40 2004, 33 40 SOE SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS E. SAVAŞ AND R. SAVAŞ Abstract. I this paper we itroduce a ew cocept of λ-strog covergece with respect to a Orlicz
More informationCommon Coupled Fixed Point of Mappings Satisfying Rational Inequalities in Ordered Complex Valued Generalized Metric Spaces
IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578, p-issn:319-765x Volume 10, Issue 3 Ver II (May-Ju 014), PP 69-77 Commo Coupled Fixed Poit of Mappigs Satisfyig Ratioal Iequalities i Ordered Complex
More informationOn the Variations of Some Well Known Fixed Point Theorem in Metric Spaces
Turkish Joural of Aalysis ad Number Theory, 205, Vol 3, No 2, 70-74 Available olie at http://pubssciepubcom/tjat/3/2/7 Sciece ad Educatio Publishig DOI:0269/tjat-3-2-7 O the Variatios of Some Well Kow
More informationMulti parameter proximal point algorithms
Multi parameter proximal poit algorithms Ogaeditse A. Boikayo a,b,, Gheorghe Moroşau a a Departmet of Mathematics ad its Applicatios Cetral Europea Uiversity Nador u. 9, H-1051 Budapest, Hugary b Departmet
More informationCOMMON FIXED POINT THEOREMS VIA w-distance
Bulleti of Mathematical Aalysis ad Applicatios ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 3, Pages 182-189 COMMON FIXED POINT THEOREMS VIA w-distance (COMMUNICATED BY DENNY H. LEUNG) SUSHANTA
More informationarxiv: v2 [math.fa] 21 Feb 2018
arxiv:1802.02726v2 [math.fa] 21 Feb 2018 SOME COUNTEREXAMPLES ON RECENT ALGORITHMS CONSTRUCTED BY THE INVERSE STRONGLY MONOTONE AND THE RELAXED (u, v)-cocoercive MAPPINGS E. SOORI Abstract. I this short
More informationON MEAN ERGODIC CONVERGENCE IN THE CALKIN ALGEBRAS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Pages 000 000 S 0002-9939(XX0000-0 ON MEAN ERGODIC CONVERGENCE IN THE CALKIN ALGEBRAS MARCH T. BOEDIHARDJO AND WILLIAM B. JOHNSON 2
More informationA Convergence Theorem for a Finite Family of Multivalued k-strictly Pseudononspreading
Thai Joural of Mathematics Volume 13 (2015) Number 3 : 581 591 http://thaijmath.i.cmu.ac.th ISSN 1686-0209 A Covergece Theorem for a Fiite Family of Multivalued k-strictly Pseudoospreadig Mappigs i R-Trees
More informationNew Iterative Method for Variational Inclusion and Fixed Point Problems
Proceedigs of the World Cogress o Egieerig 04 Vol II, WCE 04, July - 4, 04, Lodo, U.K. Ne Iterative Method for Variatioal Iclusio ad Fixed Poit Problems Yaoaluck Khogtham Abstract We itroduce a iterative
More informationCOMMON FIXED POINT THEOREMS FOR MULTIVALUED MAPS IN PARTIAL METRIC SPACES
Iteratioal Joural of Egieerig Cotemporary Mathematics ad Scieces Vol. No. 1 (Jauary-Jue 016) ISSN: 50-3099 COMMON FIXED POINT THEOREMS FOR MULTIVALUED MAPS IN PARTIAL METRIC SPACES N. CHANDRA M. C. ARYA
More informationA Common Fixed Point Theorem in Intuitionistic Fuzzy. Metric Space by Using Sub-Compatible Maps
It. J. Cotemp. Math. Scieces, Vol. 5, 2010, o. 55, 2699-2707 A Commo Fixed Poit Theorem i Ituitioistic Fuzzy Metric Space by Usig Sub-Compatible Maps Saurabh Maro*, H. Bouharjera** ad Shivdeep Sigh***
More informationA Fixed Point Result Using a Function of 5-Variables
Joural of Physical Scieces, Vol., 2007, 57-6 Fixed Poit Result Usig a Fuctio of 5-Variables P. N. Dutta ad Biayak S. Choudhury Departmet of Mathematics Begal Egieerig ad Sciece Uiversity, Shibpur P.O.:
More informationUnique Common Fixed Point Theorem for Three Pairs of Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type
Iteratioal Refereed Joural of Egieerig ad Sciece (IRJES ISSN (Olie 239-83X (Prit 239-82 Volume 2 Issue 4(April 23 PP.22-28 Uique Commo Fixed Poit Theorem for Three Pairs of Weakly Compatible Mappigs Satisfyig
More informationGeneralization of Contraction Principle on G-Metric Spaces
Global Joural of Pure ad Applied Mathematics. ISSN 0973-1768 Volume 14, Number 9 2018), pp. 1159-1165 Research Idia Publicatios http://www.ripublicatio.com Geeralizatio of Cotractio Priciple o G-Metric
More informationA constructive analysis of convex-valued demand correspondence for weakly uniformly rotund and monotonic preference
MPRA Muich Persoal RePEc Archive A costructive aalysis of covex-valued demad correspodece for weakly uiformly rotud ad mootoic preferece Yasuhito Taaka ad Atsuhiro Satoh. May 04 Olie at http://mpra.ub.ui-mueche.de/55889/
More informationA Common Fixed Point Theorem Using Compatible Mappings of Type (A-1)
Aals of Pure ad Applied Mathematics Vol. 4, No., 07, 55-6 ISSN: 79-087X (P), 79-0888(olie) Published o 7 September 07 www.researchmathsci.org DOI: http://dx.doi.org/0.457/apam.v4a8 Aals of A Commo Fixed
More informationThe Australian Journal of Mathematical Analysis and Applications
The Australia Joural of Mathematical Aalysis ad Applicatios Volume 6, Issue 1, Article 10, pp. 1-10, 2009 DIFFERENTIABILITY OF DISTANCE FUNCTIONS IN p-normed SPACES M.S. MOSLEHIAN, A. NIKNAM AND S. SHADKAM
More informationarxiv: v3 [math.fa] 1 Aug 2013
THE EQUIVALENCE AMONG NEW MULTISTEP ITERATION, S-ITERATION AND SOME OTHER ITERATIVE SCHEMES arxiv:.570v [math.fa] Aug 0 FAIK GÜRSOY, VATAN KARAKAYA, AND B. E. RHOADES Abstract. I this paper, we show that
More informationSome Fixed Point Theorems in Generating Polish Space of Quasi Metric Family
Global ad Stochastic Aalysis Special Issue: 25th Iteratioal Coferece of Forum for Iterdiscipliary Mathematics Some Fied Poit Theorems i Geeratig Polish Space of Quasi Metric Family Arju Kumar Mehra ad
More informationNEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE
UPB Sci Bull, Series A, Vol 79, Iss, 207 ISSN 22-7027 NEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE Gabriel Bercu We itroduce two ew sequeces of Euler-Mascheroi type which have fast covergece
More informationSome Common Fixed Point Theorems in Cone Rectangular Metric Space under T Kannan and T Reich Contractive Conditions
ISSN(Olie): 319-8753 ISSN (Prit): 347-671 Iteratioal Joural of Iovative Research i Sciece, Egieerig ad Techology (A ISO 397: 7 Certified Orgaizatio) Some Commo Fixed Poit Theorems i Coe Rectagular Metric
More informationConvergence of random variables. (telegram style notes) P.J.C. Spreij
Covergece of radom variables (telegram style otes).j.c. Spreij this versio: September 6, 2005 Itroductio As we kow, radom variables are by defiitio measurable fuctios o some uderlyig measurable space
More information2 Banach spaces and Hilbert spaces
2 Baach spaces ad Hilbert spaces Tryig to do aalysis i the ratioal umbers is difficult for example cosider the set {x Q : x 2 2}. This set is o-empty ad bouded above but does ot have a least upper boud
More informationKorovkin type approximation theorems for weighted αβ-statistical convergence
Bull. Math. Sci. (205) 5:59 69 DOI 0.007/s3373-05-0065-y Korovki type approximatio theorems for weighted αβ-statistical covergece Vata Karakaya Ali Karaisa Received: 3 October 204 / Revised: 3 December
More informationA Note on Convergence of a Sequence and its Applications to Geometry of Banach Spaces
Advaces i Pure Mathematics -4 doi:46/apm9 Published Olie May (http://wwwscirpg/joural/apm) A Note o Covergece of a Sequece ad its Applicatios to Geometry of Baach Spaces Abstract Hemat Kumar Pathak School
More informationProperties of Fuzzy Length on Fuzzy Set
Ope Access Library Joural 206, Volume 3, e3068 ISSN Olie: 2333-972 ISSN Prit: 2333-9705 Properties of Fuzzy Legth o Fuzzy Set Jehad R Kider, Jaafar Imra Mousa Departmet of Mathematics ad Computer Applicatios,
More informationLocal Approximation Properties for certain King type Operators
Filomat 27:1 (2013, 173 181 DOI 102298/FIL1301173O Published by Faculty of Scieces ad athematics, Uiversity of Niš, Serbia Available at: http://wwwpmfiacrs/filomat Local Approimatio Properties for certai
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 19 11/17/2008 LAWS OF LARGE NUMBERS II THE STRONG LAW OF LARGE NUMBERS
MASSACHUSTTS INSTITUT OF TCHNOLOGY 6.436J/5.085J Fall 2008 Lecture 9 /7/2008 LAWS OF LARG NUMBRS II Cotets. The strog law of large umbers 2. The Cheroff boud TH STRONG LAW OF LARG NUMBRS While the weak
More informationHÖLDER SUMMABILITY METHOD OF FUZZY NUMBERS AND A TAUBERIAN THEOREM
Iraia Joural of Fuzzy Systems Vol., No. 4, (204 pp. 87-93 87 HÖLDER SUMMABILITY METHOD OF FUZZY NUMBERS AND A TAUBERIAN THEOREM İ. C. ANAK Abstract. I this paper we establish a Tauberia coditio uder which
More informationANSWERS TO MIDTERM EXAM # 2
MATH 03, FALL 003 ANSWERS TO MIDTERM EXAM # PENN STATE UNIVERSITY Problem 1 (18 pts). State ad prove the Itermediate Value Theorem. Solutio See class otes or Theorem 5.6.1 from our textbook. Problem (18
More informationA NOTE ON INVARIANT SETS OF ITERATED FUNCTION SYSTEMS
Acta Math. Hugar., 2007 DOI: 10.1007/s10474-007-7013-6 A NOTE ON INVARIANT SETS OF ITERATED FUNCTION SYSTEMS L. L. STACHÓ ad L. I. SZABÓ Bolyai Istitute, Uiversity of Szeged, Aradi vértaúk tere 1, H-6720
More informationStatistically Convergent Double Sequence Spaces in 2-Normed Spaces Defined by Orlicz Function
Applied Mathematics, 0,, 398-40 doi:0.436/am.0.4048 Published Olie April 0 (http://www.scirp.org/oural/am) Statistically Coverget Double Sequece Spaces i -Normed Spaces Defied by Orlic Fuctio Abstract
More informationII. EXPANSION MAPPINGS WITH FIXED POINTS
Geeralizatio Of Selfmaps Ad Cotractio Mappig Priciple I D-Metric Space. U.P. DOLHARE Asso. Prof. ad Head,Departmet of Mathematics,D.S.M. College Jitur -431509,Dist. Parbhai (M.S.) Idia ABSTRACT Large umber
More informationON STATISTICAL CONVERGENCE AND STATISTICAL MONOTONICITY
Aales Uiv. Sci. Budapest., Sect. Comp. 39 (203) 257 270 ON STATISTICAL CONVERGENCE AND STATISTICAL MONOTONICITY E. Kaya (Mersi, Turkey) M. Kucukasla (Mersi, Turkey) R. Wager (Paderbor, Germay) Dedicated
More informationBETWEEN QUASICONVEX AND CONVEX SET-VALUED MAPPINGS. 1. Introduction. Throughout the paper we denote by X a linear space and by Y a topological linear
BETWEEN QUASICONVEX AND CONVEX SET-VALUED MAPPINGS Abstract. The aim of this paper is to give sufficiet coditios for a quasicovex setvalued mappig to be covex. I particular, we recover several kow characterizatios
More informationResearch Article A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property
Discrete Dyamics i Nature ad Society Volume 2011, Article ID 360583, 6 pages doi:10.1155/2011/360583 Research Article A Note o Ergodicity of Systems with the Asymptotic Average Shadowig Property Risog
More informationChapter 3. Strong convergence. 3.1 Definition of almost sure convergence
Chapter 3 Strog covergece As poited out i the Chapter 2, there are multiple ways to defie the otio of covergece of a sequece of radom variables. That chapter defied covergece i probability, covergece i
More informationEquivalent Banach Operator Ideal Norms 1
It. Joural of Math. Aalysis, Vol. 6, 2012, o. 1, 19-27 Equivalet Baach Operator Ideal Norms 1 Musudi Sammy Chuka Uiversity College P.O. Box 109-60400, Keya sammusudi@yahoo.com Shem Aywa Maside Muliro Uiversity
More informationThe log-behavior of n p(n) and n p(n)/n
Ramauja J. 44 017, 81-99 The log-behavior of p ad p/ William Y.C. Che 1 ad Ke Y. Zheg 1 Ceter for Applied Mathematics Tiaji Uiversity Tiaji 0007, P. R. Chia Ceter for Combiatorics, LPMC Nakai Uivercity
More informationarxiv: v2 [math.fa] 28 Apr 2014
arxiv:14032546v2 [mathfa] 28 Apr 2014 A PICARD-S HYBRID TYPE ITERATION METHOD FOR SOLVING A DIFFERENTIAL EQUATION WITH RETARDED ARGUMENT FAIK GÜRSOY AND VATAN KARAKAYA Abstract We itroduce a ew iteratio
More informationDefinition 4.2. (a) A sequence {x n } in a Banach space X is a basis for X if. unique scalars a n (x) such that x = n. a n (x) x n. (4.
4. BASES I BAACH SPACES 39 4. BASES I BAACH SPACES Sice a Baach space X is a vector space, it must possess a Hamel, or vector space, basis, i.e., a subset {x γ } γ Γ whose fiite liear spa is all of X ad
More informationCharacterizations Of (p, α)-convex Sequences
Applied Mathematics E-Notes, 172017, 77-84 c ISSN 1607-2510 Available free at mirror sites of http://www.math.thu.edu.tw/ ame/ Characterizatios Of p, α-covex Sequeces Xhevat Zahir Krasiqi Received 2 July
More informationINVERSE THEOREMS OF APPROXIMATION THEORY IN L p,α (R + )
Electroic Joural of Mathematical Aalysis ad Applicatios, Vol. 3(2) July 2015, pp. 92-99. ISSN: 2090-729(olie) http://fcag-egypt.com/jourals/ejmaa/ INVERSE THEOREMS OF APPROXIMATION THEORY IN L p,α (R +
More informationAre adaptive Mann iterations really adaptive?
MATHEMATICAL COMMUNICATIONS 399 Math. Commu., Vol. 4, No. 2, pp. 399-42 (2009) Are adaptive Ma iteratios really adaptive? Kamil S. Kazimierski, Departmet of Mathematics ad Computer Sciece, Uiversity of
More informationMAT1026 Calculus II Basic Convergence Tests for Series
MAT026 Calculus II Basic Covergece Tests for Series Egi MERMUT 202.03.08 Dokuz Eylül Uiversity Faculty of Sciece Departmet of Mathematics İzmir/TURKEY Cotets Mootoe Covergece Theorem 2 2 Series of Real
More informationMAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES
Commu Korea Math Soc 26 20, No, pp 5 6 DOI 0434/CKMS20265 MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES Wag Xueju, Hu Shuhe, Li Xiaoqi, ad Yag Wezhi Abstract Let {X, } be a sequece
More informationResearch Article Moment Inequality for ϕ-mixing Sequences and Its Applications
Hidawi Publishig Corporatio Joural of Iequalities ad Applicatios Volume 2009, Article ID 379743, 2 pages doi:0.55/2009/379743 Research Article Momet Iequality for ϕ-mixig Sequeces ad Its Applicatios Wag
More informationSome Tauberian theorems for weighted means of bounded double sequences
A. Ştiiţ. Uiv. Al. I. Cuza Iaşi. Mat. N.S. Tomul LXIII, 207, f. Some Tauberia theorems for weighted meas of bouded double sequeces Cemal Bele Received: 22.XII.202 / Revised: 24.VII.203/ Accepted: 3.VII.203
More informationAPPROXIMATION BY BERNSTEIN-CHLODOWSKY POLYNOMIALS
Hacettepe Joural of Mathematics ad Statistics Volume 32 (2003), 1 5 APPROXIMATION BY BERNSTEIN-CHLODOWSKY POLYNOMIALS E. İbili Received 27/06/2002 : Accepted 17/03/2003 Abstract The weighted approximatio
More informationRiesz-Fischer Sequences and Lower Frame Bounds
Zeitschrift für Aalysis ud ihre Aweduge Joural for Aalysis ad its Applicatios Volume 1 (00), No., 305 314 Riesz-Fischer Sequeces ad Lower Frame Bouds P. Casazza, O. Christese, S. Li ad A. Lider Abstract.
More informationThe Choquet Integral with Respect to Fuzzy-Valued Set Functions
The Choquet Itegral with Respect to Fuzzy-Valued Set Fuctios Weiwei Zhag Abstract The Choquet itegral with respect to real-valued oadditive set fuctios, such as siged efficiecy measures, has bee used i
More informationLecture 19: Convergence
Lecture 19: Covergece Asymptotic approach I statistical aalysis or iferece, a key to the success of fidig a good procedure is beig able to fid some momets ad/or distributios of various statistics. I may
More informationA Characterization of Compact Operators by Orthogonality
Australia Joural of Basic ad Applied Scieces, 5(6): 253-257, 211 ISSN 1991-8178 A Characterizatio of Compact Operators by Orthogoality Abdorreza Paahi, Mohamad Reza Farmai ad Azam Noorafa Zaai Departmet
More informationIntroduction to Optimization Techniques
Itroductio to Optimizatio Techiques Basic Cocepts of Aalysis - Real Aalysis, Fuctioal Aalysis 1 Basic Cocepts of Aalysis Liear Vector Spaces Defiitio: A vector space X is a set of elemets called vectors
More informationSOME GENERALIZATIONS OF OLIVIER S THEOREM
SOME GENERALIZATIONS OF OLIVIER S THEOREM Alai Faisat, Sait-Étiee, Georges Grekos, Sait-Étiee, Ladislav Mišík Ostrava (Received Jauary 27, 2006) Abstract. Let a be a coverget series of positive real umbers.
More informationMATH301 Real Analysis (2008 Fall) Tutorial Note #7. k=1 f k (x) converges pointwise to S(x) on E if and
MATH01 Real Aalysis (2008 Fall) Tutorial Note #7 Sequece ad Series of fuctio 1: Poitwise Covergece ad Uiform Covergece Part I: Poitwise Covergece Defiitio of poitwise covergece: A sequece of fuctios f
More informationResearch Article Invariant Statistical Convergence of Sequences of Sets with respect to a Modulus Function
Hidawi Publishig Corporatio Abstract ad Applied Aalysis, Article ID 88020, 5 pages http://dx.doi.org/0.55/204/88020 Research Article Ivariat Statistical Covergece of Sequeces of Sets with respect to a
More informationfor all x ; ;x R. A ifiite sequece fx ; g is said to be ND if every fiite subset X ; ;X is ND. The coditios (.) ad (.3) are equivalet for =, but these
sub-gaussia techiques i provig some strog it theorems Λ M. Amii A. Bozorgia Departmet of Mathematics, Faculty of Scieces Sista ad Baluchesta Uiversity, Zaheda, Ira Amii@hamoo.usb.ac.ir, Fax:054446565 Departmet
More informationResearch Article Variant Gradient Projection Methods for the Minimization Problems
Abstract ad Applied Aalysis Volume 2012, Article ID 792078, 16 pages doi:10.1155/2012/792078 Research Article Variat Gradiet Projectio Methods for the Miimizatio Problems Yoghog Yao, 1 Yeog-Cheg Liou,
More informationCommon Fixed Points for Multivalued Mappings
Advaces i Applied Mathematical Bioscieces. ISSN 48-9983 Volume 5, Number (04), pp. 9-5 Iteratioal Research Publicatio House http://www.irphouse.com Commo Fixed Poits for Multivalued Mappigs Lata Vyas*
More informationIntroduction to Probability. Ariel Yadin
Itroductio to robability Ariel Yadi Lecture 2 *** Ja. 7 ***. Covergece of Radom Variables As i the case of sequeces of umbers, we would like to talk about covergece of radom variables. There are may ways
More informationReal Numbers R ) - LUB(B) may or may not belong to B. (Ex; B= { y: y = 1 x, - Note that A B LUB( A) LUB( B)
Real Numbers The least upper boud - Let B be ay subset of R B is bouded above if there is a k R such that x k for all x B - A real umber, k R is a uique least upper boud of B, ie k = LUB(B), if () k is
More informationBIRKHOFF ERGODIC THEOREM
BIRKHOFF ERGODIC THEOREM Abstract. We will give a proof of the poitwise ergodic theorem, which was first proved by Birkhoff. May improvemets have bee made sice Birkhoff s orgial proof. The versio we give
More informationAlmost Surjective Epsilon-Isometry in The Reflexive Banach Spaces
CAUCHY JURNAL MATEMATIKA MURNI DAN APLIKASI Volume 4 (4) (2017), Pages 167-175 p-issn: 2086-0382; e-issn: 2477-3344 Almost Surjective Epsilo-Isometry i The Reflexive Baach Spaces Miaur Rohma Departmet
More informationlim za n n = z lim a n n.
Lecture 6 Sequeces ad Series Defiitio 1 By a sequece i a set A, we mea a mappig f : N A. It is customary to deote a sequece f by {s } where, s := f(). A sequece {z } of (complex) umbers is said to be coverget
More informationSequences and Series of Functions
Chapter 6 Sequeces ad Series of Fuctios 6.1. Covergece of a Sequece of Fuctios Poitwise Covergece. Defiitio 6.1. Let, for each N, fuctio f : A R be defied. If, for each x A, the sequece (f (x)) coverges
More informationAvailable online at J. Math. Comput. Sci. 2 (2012), No. 3, ISSN:
Available olie at http://scik.org J. Math. Comput. Sci. 2 (202, No. 3, 656-672 ISSN: 927-5307 ON PARAMETER DEPENDENT REFINEMENT OF DISCRETE JENSEN S INEQUALITY FOR OPERATOR CONVEX FUNCTIONS L. HORVÁTH,
More informationResearch Article Approximate Riesz Algebra-Valued Derivations
Abstract ad Applied Aalysis Volume 2012, Article ID 240258, 5 pages doi:10.1155/2012/240258 Research Article Approximate Riesz Algebra-Valued Derivatios Faruk Polat Departmet of Mathematics, Faculty of
More informationON BI-SHADOWING OF SUBCLASSES OF ALMOST CONTRACTIVE TYPE MAPPINGS
Vol. 9, No., pp. 3449-3453, Jue 015 Olie ISSN: 190-3853; Prit ISSN: 1715-9997 Available olie at www.cjpas.et ON BI-SHADOWING OF SUBCLASSES OF ALMOST CONTRACTIVE TYPE MAPPINGS Awar A. Al-Badareh Departmet
More informationSolutions to home assignments (sketches)
Matematiska Istitutioe Peter Kumli 26th May 2004 TMA401 Fuctioal Aalysis MAN670 Applied Fuctioal Aalysis 4th quarter 2003/2004 All documet cocerig the course ca be foud o the course home page: http://www.math.chalmers.se/math/grudutb/cth/tma401/
More informationFIXED POINTS AND BEST APPROXIMATION IN MENGER CONVEX METRIC SPACES
ARCHIVUM MATHEMATICUM BRNO Tomus 41 2005, 389 397 FIXED POINTS AND BEST APPROXIMATION IN MENGER CONVEX METRIC SPACES ISMAT BEG AND MUJAHID ABBAS Abstract. We obtai ecessary coditios for the existece of
More informationBounds for the Positive nth-root of Positive Integers
Pure Mathematical Scieces, Vol. 6, 07, o., 47-59 HIKARI Ltd, www.m-hikari.com https://doi.org/0.988/pms.07.7 Bouds for the Positive th-root of Positive Itegers Rachid Marsli Mathematics ad Statistics Departmet
More informationFall 2013 MTH431/531 Real analysis Section Notes
Fall 013 MTH431/531 Real aalysis Sectio 8.1-8. Notes Yi Su 013.11.1 1. Defiitio of uiform covergece. We look at a sequece of fuctios f (x) ad study the coverget property. Notice we have two parameters
More informationMath Solutions to homework 6
Math 175 - Solutios to homework 6 Cédric De Groote November 16, 2017 Problem 1 (8.11 i the book): Let K be a compact Hermitia operator o a Hilbert space H ad let the kerel of K be {0}. Show that there
More informationOn a fixed point theorems for multivalued maps in b-metric space. Department of Mathematics, College of Science, University of Basrah,Iraq
Basrah Joural of Sciece (A) Vol.33(),6-36, 05 O a fixed poit theorems for multivalued maps i -metric space AMAL M. HASHM DUAA L.BAQAIR Departmet of Mathematics, College of Sciece, Uiversity of Basrah,Iraq
More informationA 2nTH ORDER LINEAR DIFFERENCE EQUATION
A 2TH ORDER LINEAR DIFFERENCE EQUATION Doug Aderso Departmet of Mathematics ad Computer Sciece, Cocordia College Moorhead, MN 56562, USA ABSTRACT: We give a formulatio of geeralized zeros ad (, )-discojugacy
More informationA GENERALIZED MEAN PROXIMAL ALGORITHM FOR SOLVING GENERALIZED MIXED EQUILIBRIUM PROBLEMS (COMMUNICATED BY MARTIN HERMANN)
Bulleti of Mathematical Aalysis ad Applicatios ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 7 Issue 1 (2015), Pages 1-11 A GENERALIZED MEAN PROXIMAL ALGORITHM FOR SOLVING GENERALIZED MIXED EQUILIBRIUM
More informationAPPROXIMATION PROPERTIES OF STANCU TYPE MEYER- KÖNIG AND ZELLER OPERATORS
Hacettepe Joural of Mathematics ad Statistics Volume 42 (2 (2013, 139 148 APPROXIMATION PROPERTIES OF STANCU TYPE MEYER- KÖNIG AND ZELLER OPERATORS Mediha Örkcü Received 02 : 03 : 2011 : Accepted 26 :
More information62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +
62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of
More informationGeneralized Dynamic Process for Generalized Multivalued F-contraction of Hardy Rogers Type in b-metric Spaces
Turkish Joural of Aalysis a Number Theory, 08, Vol. 6, No., 43-48 Available olie at http://pubs.sciepub.com/tjat/6// Sciece a Eucatio Publishig DOI:0.69/tjat-6-- Geeralize Dyamic Process for Geeralize
More informationStrong Convergence Theorems for Nonself I-Asymptotically Quasi-Nonexpansive Mappings 1
Applied Mathematical Sciences, Vol. 2, 2008, no. 19, 919-928 Strong Convergence Theorems for Nonself I-Asymptotically Quasi-Nonexpansive Mappings 1 Si-Sheng Yao Department of Mathematics, Kunming Teachers
More informationAN EXTENSION OF SIMONS INEQUALITY AND APPLICATIONS. Robert DEVILLE and Catherine FINET
2001 vol. XIV, um. 1, 95-104 ISSN 1139-1138 AN EXTENSION OF SIMONS INEQUALITY AND APPLICATIONS Robert DEVILLE ad Catherie FINET Abstract This article is devoted to a extesio of Simos iequality. As a cosequece,
More informationOn common fixed point theorems for weakly compatible mappings in Menger space
Available olie at www.pelagiaresearchlibrary.com Advaces i Applied Sciece Research, 2016, 7(5): 46-53 ISSN: 0976-8610 CODEN (USA): AASRFC O commo fixed poit theorems for weakly compatible mappigs i Meger
More informationIT is well known that Brouwer s fixed point theorem can
IAENG Iteratioal Joural of Applied Mathematics, 4:, IJAM_4 0 Costructive Proof of Brouwer s Fixed Poit Theorem for Sequetially Locally No-costat ad Uiformly Sequetially Cotiuous Fuctios Yasuhito Taaka,
More informationOn Summability Factors for N, p n k
Advaces i Dyamical Systems ad Applicatios. ISSN 0973-532 Volume Number 2006, pp. 79 89 c Research Idia Publicatios http://www.ripublicatio.com/adsa.htm O Summability Factors for N, p B.E. Rhoades Departmet
More informationStatistical Approximation Properties of a Generalization of Positive Linear Operators
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 5 No. 0 75-87 ISSN 307-5543 www.ejpam.com SPECIAL ISSUE FOR THE INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND ALGEBRA 9 JUNE - 0 JULY 0 ISTANBUL
More informationTauberian Conditions in Terms of General Control Modulo of Oscillatory Behavior of Integer Order of Sequences
Iteratioal Mathematical Forum, 2, 2007, o. 20, 957-962 Tauberia Coditios i Terms of Geeral Cotrol Modulo of Oscillatory Behavior of Iteger Order of Sequeces İ. Çaak Departmet of Math., Ada Mederes Uiversity,
More informationM17 MAT25-21 HOMEWORK 5 SOLUTIONS
M17 MAT5-1 HOMEWORK 5 SOLUTIONS 1. To Had I Cauchy Codesatio Test. Exercise 1: Applicatio of the Cauchy Codesatio Test Use the Cauchy Codesatio Test to prove that 1 diverges. Solutio 1. Give the series
More information